By integrating a free-standing cadmium sulfide (CdS) nanowire onto a silicon nitride (SiN) photonic chip, we demonstrate a highly compact on-chip single-mode CdS nanowire laser. The mode selection is realized using a Mach-Zehnder interferometer (MZI) structure. When the pumping intensity exceeds the lasing threshold of 4.9 kW/cm2, on-chip single-mode lasing at～518.9 nm is achieved with a linewidth of 0.1 nm and a side-mode suppression ratio of up to a factor of 20 (13 dB). The output of the nanowire laser is channelled into an on-chip SiN waveguide with high efficiency (up to 58％) by evanescent coupling, and the directional coupling ratio between the two output ports can be varied from 90 to 10％by predesigning the coupling length of the SiN waveguide. Our results open new opportunities for both nanowire photonic devices and on-chip light sources and may pave the way towards a new category of hybrid nanolasers for chip-integrated applications.